Understand the idea.
Pairs decide whether a number is even
Try making pairs without breaking any objects. An even number makes complete pairs; an odd number leaves exactly one object without a partner. Zero is even because it has no unpaired object.
Tens, hundreds and thousands already make complete pairs, so only the ones digit can leave a leftover. Numbers ending in , , , or are even; the other possible ones digits make odd numbers.
Use pairs to explain a rule
Joining two even groups joins complete pairs. Joining an even group and an odd group leaves the odd group's single leftover. Joining two odd groups lets their two leftovers form a pair. This explains the addition patterns without calculating every total.
For multiplication, an even number of groups can be paired into matching groups. If each group has an even size, pair objects within every group instead. Only an odd number of odd-sized groups leaves one object unpaired, giving an odd product.
See the method in action.
Classify a large number
Is 8,137 odd or even? Explain without drawing 8,137 dots.
Worked solution
- 1
Separate the ones from the other places.
The first part is a whole number of tens, and every ten makes complete pairs.
- 2
Pair the seven ones.
Three pairs use six ones and leave one without a partner.
- 3
Classify the entire number.
The tens leave no leftover, so the one unpaired object makes 8,137 odd.
Odd, because it ends in 7.
Predict a total
Without adding fully, decide whether 215 + 387 is odd or even.
Worked solution
- 1
Read each ones digit.
215 ends in 5 and 387 ends in 7, so both numbers are odd.
- 2
Join their leftover objects.
Each odd group leaves one object, and these two objects form a pair.
- 3
Classify the sum.
All objects now belong to pairs, even without finding the full total.
Even. Odd + odd is even.
Try it yourself.
Check your understanding
Must 6 × 13 be odd or even?
Show answer & reasoning
Even.
The product is even: six groups of thirteen can be paired into three double-groups. Each double-group contains two matching sets, so no object is left unpaired.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- List the even numbers: 17, 28, 40, 53, 66.1 mark
- Is 7,205 odd or even? Give a reason.1 mark
- Complete the rule: is ____.1 mark
- Without finding the exact total, classify .2 marks
- Give two different odd numbers whose sum is 20.2 marks
- A learner says is always even. Use a calculation to disprove this and state the correct rule.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- List the even numbers: 17, 28, 40, 53, 66.1 mark
Their ones digits are 8, 0 and 6.
28, 40 and 66. - Is 7,205 odd or even? Give a reason.1 mark
The last digit determines the leftover after pairing.
Odd, because its ones digit is 5. - Complete the rule: is ____.1 mark
Joining two groups made entirely of pairs still gives complete pairs.
Even. - Without finding the exact total, classify .2 marks
4,018 is even and 723 is odd.
is odd.
Odd. - Give two different odd numbers whose sum is 20.2 marks
Check that both numbers are odd and their sum is 20.
For example, 7 and 13. Other valid pairs include 1 and 19, 3 and 17, or 9 and 11. - A learner says is always even. Use a calculation to disprove this and state the correct rule.2 marks
Both factors are odd, but 15 is odd: the proposed rule is false.
An odd number of odd groups leaves one object unpaired.
For example, . is odd.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.
Official curriculum source ↗